Problem: Solve for $x$ and $y$ using substitution. ${-x-5y = -12}$ ${x = 4y+3}$
Answer: Since $x$ has already been solved for, substitute $4y+3$ for $x$ in the first equation. ${-}{(4y+3)}{- 5y = -12}$ Simplify and solve for $y$ $-4y-3 - 5y = -12$ $-9y-3 = -12$ $-9y-3{+3} = -12{+3}$ $-9y = -9$ $\dfrac{-9y}{{-9}} = \dfrac{-9}{{-9}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = 4y+3}\thinspace$ to find $x$ ${x = 4}{(1)}{ + 3}$ $x = 4 + 3$ ${x = 7}$ You can also plug ${y = 1}$ into $\thinspace {-x-5y = -12}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(1)}{= -12}$ ${x = 7}$